Vertices as particles?
You used to be able to render vertices as halos. That only worked with the old Blender Internal renderer which was completely scrapped. I miss the halos. 
Anyways, there is an alternative option called Point Density, I'm not going into this here, because it renders slowly and is not well suited for your situation. 
I suggest you use icospheres, or stick to the cubes if they looked good enough.